dynamic characteristics of hagia sophia in istanbul before ... · hagia sophia is a huge structure...
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_______________________________
1 System and Data Research, Tokyo, Japan
1
Dynamic Characteristics of Hagia Sophia in Istanbul
before and after the 1999 Kocaeli Earthquake
by Microtremor Measurements Yutaka Nakamura
1, Tsutomu Sato
1 and Jun Saita
1
Abstract Hagia Sophia is a huge structure rebuilt in 537AD with a big dome.
It has been suffered accidents as collapsing the dome repeatedly by
earthquakes but the original shape has been remained miraculously. A
Mw7.4 earthquake about 100km away attacked and affected Hagia
Sophia in August 17, 1999. We had measured microtremor of some
structures in Istanbul including Hagia Sophia two months before the
earthquake by chance. Two weeks after the earthquake, we had meas-
ured at almost same place again. Hagia Sophia was affected severely
estimated from the predominant frequency sift. This fact has been al-
ready reported and this time the situation of the changing dynamic
characteristics before and after the earthquake is reanalysed with 48
points from the response spectra, vibration locus and mode and so on.
As a result, the response spectra of the main structure shows many
peaks, mainly one clear peak for EW direction and two peaks for NS
direction. Amplification factors of EW component are larger than that
of NS component and both of them at south side are larger than that at
north side. Amplification factors decreased obviously after the earth-
quake for entire the EW component. But for NS direction, it was al-
most same at the dome cornice, increased at southern side of 2nd
cor-
nice or gallery level (hereafter 3F or 2F respectively) and decreased
drastically at northern side of 3F or 2F. The torsional vibration in the
horizontal plane can be detected by the simultaneous measurement at
east and west main pears on 2F and 3F. It shows complexities as some
is confirmed in a south-north couple and the other is confirmed only at
the one part. It shows that each part moves with a certain level of de-
gree of freedom and suggests the progress of degradation.
Dynamic Characteristics of Hagia Sophia in Istanbul Before and After the 1999 Kocaeli Earthquake by Microtremor Measurements
Y. Nakamura, T. Sato and J. Saita
System and Data Research
Dynamic Characteristics of
Hagia Sophia in Istanbul
Before and After the 1999 Kocaeli Earthquake
by Microtremor Measurements
Yutaka NAKAMURA1), Tsutomu Sato1) and Jun Saita1)
1) System and Data Research, Tokyo, Japan.
System and Data Research
Outline of Hagia Sophia Museum
Hagia Sophia Museum construction begun in 532, dedicated in 537 and received its definitive form
in 562, as a principal church of Byzantine empire and converted to a royal mosque in 1453. It
contains four brick arches from stone piers that offer primary support for a 31m diameter central
dome and two semi-domes. It has four main piers supporting the corners of the dome base and four
main arches that spring from these piers and support the edges of dome base (Cakmak et. al., 1995).
It has a dimension of free internal space 30m wide, 80m long, 56m high. During its history it was
affected by many earthquakes resulting in several reconstruction of different parts of the main dome
and repair of some structural elements (Durukal et. al., 1994). Structure exhibits large deformations
in its piers and arches resulting from the material properties. Main piers inclined away from vertical
45cm along the short axis and lean backward an average of 15cm along the long axis.
After: Sept. 1999 Before: Oｃｔ.1998
System and Data Research
Introduction
This presentation is about the result of the microtremor measurement
at Hagia Sophia museum in Istanbul conducted at 8th and 9th June
1999 and at 3rd September 1999, before and after the Kocaeli
earthquake, occurred in 17th August 1999, with a focus on the change
after the earthquake.
Contents
Locations of Microtremor Measurement
Measurement and Analysis
General Characteristics
Change of Characteristics by The Earthquake
Vulnerability Assessment
System and Data Research
Locations of Microtremor Measurement
These figures show measurement locations on the plane, the side
and front cross sections of the museum. Outside of the museum,
measurement points were set 7 points on the ground. And inside
of the museum, measurement points were set 16 points at the
first floor (1F), 16 points at the gallery level (2F), 8 points at the
second cornice (3F) and 8 points at main dome cornice (D). Total number is 48 inside.
Dome
3F (2nd
cornice)
2F (Gallery)
1st Floor
Ground
Dome
3F (2nd Cornice)
2F (Gallery)
1st Floor
Ground
10m
G1
G2 G3
G4
G5 G6
G7
1F1 1F2 1F3 1F4
1F5
1F6
1F7
1F8
1F9
1F10
1F11 1F12 1F13 1F14
1F15
1F16 2F16
2F6
2F5
2F4 2F3
2F1 2F2
2F7
2F8
2F9
2F10
2F13 2F14
2F11 2F12 2F15
simultaneous measurement
E
SE S
SW
W
NW N
NE
3F1 3F2
3F8
3F9
3F13 3F14
3F6
3F16
10m
System and Data Research
Microtremor Locus in Velocity Amplitude of Before and After After
This slide indicates velocity loci of measured microtremor corresponding to each measurement point. Please
notice that these loci were not measured simultaneously. Loci are extremely small with almost same level at
all the points at 1F, however on the 2F, they are small at the points at the corner of southeast or north and
large at the center. The extent of loci over 2F is almost same and loci on the dome cornice locate radially and
the east-west motion is predominated at the west end. Before the earthquake, the loci is predominantly large
at south of the dome cornice. After the earthquake, the loci are averaged especially at the dome cornice and
they become large at the northern side and relatively large at western side as the building motion. Additionally,
the north-south motion predominates at the center of the gallery level 2F.
Before
2F 1F
2F
2F
2F 2F
2F 2F
2F
2F
2F
System and Data Research
Microtremor Locus in Velocity Amplitude of Before and After
Before After
The vertical motion predominates on
the east and west half dome, and the
vibration seems to be rocking
vibration on the north-south arch.
Before
After
System and Data Research
Transfer Functions of EW component after the Event
0.1
1
10
100
0.1 1 10
DWDNW3F12F11F1
0.1
1
10
100
0.1 1 10
DNDNE3F22F21F2
0.1
1
10
100
0.1 1 10
DSDSW3F132F131F13
0.1
1
10
100
0.1 1 10
DEDSE3F142F141F14
0.1
1
10
100
0.1 1 10
3F8
2F8
1F8
0.1
1
10
100
0.1 1 10
3F9
2F9
1F9
0.1
1
10
100
0.1 1 10
3F6
2F6
1F6
0.1
1
10
100
0.1 1 10
3F16
2F16
1F16
0.1
1
10
100
0.1 1 10
2F3
1F3
0.1
1
10
100
0.1 1 10
2F4
1F4
0.1
1
10
100
0.1 1 10
2F5
1F5
0.1
1
10
100
0.1 1 10
2F7
1F7
0.1
1
10
100
0.1 1 10
2F10
1F10
0.1
1
10
100
0.1 1 10
2F11
1F11
0.1
1
10
100
0.1 1 10
2F12
1F12
0.1
1
10
100
0.1 1 10
2F15
1F15
Frequency in Hz Frequency in Hz Frequency in Hz Frequency in Hz
Am
plifi
catio
n F
acto
r
NW 2nd pier
SW 2nd pier
NE 2nd pier
SE 2nd pier
NW main pier and dome NE main pier and dome
SW main pier and dome SE main pier and dome
NW corner
SW corner
NE corner
SE corner SW buttress pier SE buttress pier
NW buttress pier NE buttress pier
Microtremor spectrum was derived as the average of three Fourier spectrums with 40.96 seconds long.
The transfer function for each measurement point is derived as division of the microtremor spectrum of
each point by that of corresponding 1F point. This figure indicates the amplification spectrum of the 20
points on the horizontal plane placing at the point corresponding location including points at the dome.
System and Data Research
Transfer Functions of Main Dome and Piers, Before and After
At the dome cornice, there are one clear peak as 1st modal frequency at EW component and two
peaks as 2nd and 3rd modal frequencies at NS component. However peaks at EW component can be
recognized at all the columns before the earthquake, they can be recognized only at the southern side
after the earthquake. This trend is seemed at the two peaks of NS component and the southern side
becomes to be relatively easy to shake after the earthquake.
0.1
1
10
100
1 10
3F13F23F133F14
1
10
100
1000
1 10
DN DNEDE DSEDS DSWDW DNW
0.1
1
10
100
1 10
2F12F22F132F14
0.1
1
10
100
1 10
3F13F23F133F14
1
10
100
1000
1 10
DN DNE
DE DSE
DS DSW
DW DNW
0.1
1
10
100
1 10
2F12F22F132F14
0.1
1
10
100
1 10
3F1
3F2
3F13
3F14
0.1
1
10
100
1 10
DN DNEDE DSEDS DSWDW DNW
0.1
1
10
100
1 10
2F1
2F2
2F13
2F14
0.1
1
10
100
1 10
3F13F23F133F14
0.1
1
10
100
1 10
DN DNEDE DSEDS DSWDW DNW
0.1
1
10
100
1 10
2F12F22F132F14
Frequency in Hz
EW EW NS NS
Before After
Frequency in Hz Frequency in Hz Frequency in Hz A
mpl
ifica
tion
Fac
tor
Dome Dome Dome Dome
3F
main pier
3F 3F 3F
1st m
odal
freq
.
2nd m
odal
freq
. 3rd
mod
al fr
eq.
1st m
odal
freq
.
2nd m
odal
freq
. 3rd
mod
al fr
eq.
2F
main Pier 2F 2F 2F
System and Data Research
The predominant frequency during earthquake event is 1.38 – 1.61 Hz for EW
component and 1.53 – 1.79 Hz for NS component after Durukal et al. (2003). Contrary
to this, that of microtremor is rather high. It is considered that the predominant
frequency during the Kocaeli earthquake decreased more than 25% against that of
microtremor, and the change of the predominant frequency remained at around 8% by
the microtremor measurement just after this earthquake. And the result of the analysis
on the earthquake motion records by Durukal et al. (2003) suggests the possibility of the
quickly decrease and restitution of the predominant frequency by the earthquake motion.
Change of Predominant Frequency
date 1991 12-Dec-93 1999.6 17-Aug-99 1999.9 Sep. to Dec. 2000
MT or EQ microtremor Eq. microtremor Kocaeli Eq. microtremor Eqs. microtremor
EW 1.85 1.56 1.90 ? 1.76 1.38-1.61 1.75
NS 2.10 1.77 2.20 ? 2.03 1.53-1.79 2.10
unit Hz Hz Hz Hz Hz Hz Hz
by Erdik etal by Erdik etal
Mb4.8, Δ=59km Mw7.4, Δ=97km
1.41?
1.62?
M4.4 – M7.2
Durukal et.al.(2003) Durukal et.al.(2003)
System and Data Research
Amplification Mode of 1st Modal Frequency (EW comp.)
0
5
10
15
20
25
30
35
40
45
0 100 200 300
Main Dome
0
5
10
15
20
25
0 50 100
West and East
0
5
10
15
0 20 40
North and South
0
5
10
15
0 100 200 300
Around 3
0
5
10
15
0 100 200 300
Around 4
0
5
10
15
0 100 200 300
Around 5
0
5
10
15
0 100 200 300
Around 7
0
5
10
15
0 100 200 300
Around 10
0
5
10
15
0 100 200 300
Around 11
0
5
10
15
0 100 200 300
Around 12
0
5
10
15
0 100 200 300
Around 15
0
5
10
15
20
25
0 100 200 300
West North
0
5
10
15
20
25
0 100 200 300
West South
0
5
10
15
20
25
0 100 200 300
East North
0
5
10
15
20
25
0 100 200 300
East South
0
5
10
15
20
25
30
35
40
45
0 100 200 300
Main Dome W and NW
0
5
10
15
20
25
30
35
40
45
0 100 200 300
Main Dome N and NE
0
5
10
15
20
25
30
35
40
45
0 100 200 300
Main Dome S and SW
0
5
10
15
20
25
30
35
40
45
0 100 200 300
Main Dome E and SE
Hei
ght i
n m
Amplification Factor
1.9043Hz Before
EW
DW DN
DS
NW Main Pier
SW Main Pier
SE Main Pier
NE Main Pier
N
S
W E
1F
2F 3F
D
300
300
100
40
300
300
300
-7.7% 0
5
10
15
20
25
30
35
40
45
0 100 200 300
Main Dome
0
5
10
15
20
25
0 50 100
West and East
0
5
10
15
0 20 40
North and South
0
5
10
15
0 50 100
Around 3
0
5
10
15
0 50 100
Around 4
0
5
10
15
0 50 100
Around 5
0
5
10
15
0 50 100
Around 7
0
5
10
15
0 50 100
Around 10
0
5
10
15
0 50 100
Around 11
0
5
10
15
0 50 100
Around 12
0
5
10
15
0 50 100
Around 15
0
5
10
15
20
25
0 50 100
West North
0
5
10
15
20
25
0 50 100
West South
0
5
10
15
20
25
0 50 100
East North
0
5
10
15
20
25
0 50 100
East South
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome W and NW
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome N and NE
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome S and SW
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome E and SE
Hei
ght i
n m
Amplification Factor
1.7578Hz
After
EW
DW DN
DS
NW
SW SE
NE
1F
2F
3F
D
N
S
W E
300
100
40
100
100
100
100
NW
2nd Pier
SW
2nd Pier
NE
2nd Pier
SE
2nd Pier
NW corner
SW corner
NE corner
SE corner SW
buttress pier SE
buttress pier
NW
buttress pier
NE
buttress pier
NW
2nd Pier
SW
2nd Pier
NE
2nd Pier
SE
2nd Pier
NW corner NE corner NW
buttress pier
NE
buttress pier
SW corner SE corner SW
buttress pier SE
buttress pier
This figure shows the amplification mode of the 1st modal frequency derived from the
amplification spectrum corresponding to the location on the plane. Vertical axis is height of
the location, horizontal axis is amplification factor. The amplification characteristics show
that it is large not only at the southern side but also western side. Especially it becomes
large at the main Piers and the dome at south-west part. Although the amplification factor
becomes totally small after the earthquake, these characteristics are not changed.
System and Data Research
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome
0
5
10
15
20
25
0 5 10 15
West and East
0
5
10
15
0 5 10 15
North and South
0
5
10
15
0 50 100
Around 3
0
5
10
15
0 50 100
Around 4
0
5
10
15
0 50 100
Around 5
0
5
10
15
0 50 100
Around 7
0
5
10
15
0 50 100
Around 10
0
5
10
15
0 50 100
Around 11
0
5
10
15
0 50 100
Around 12
0
5
10
15
0 50 100
Around 15
0
5
10
15
20
25
0 50 100
West North
0
5
10
15
20
25
0 50 100
West South
0
5
10
15
20
25
0 50 100
East North
0
5
10
15
20
25
0 50 100
East South
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome W and NW
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome N and NE
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome S and SW
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome E and SE
Hei
ght i
n m
Amplification Factor
2.1973Hz Before
NS
DW DN
DS
NW
SW SE
NE
N
S
W E
1F
2F
3F
D
100
15
15
100
100
100
100
0
5
10
15
20
25
30
35
40
45
0 50 100
Maiin Dome
0
5
10
15
20
25
0 5 10 15
West and East
0
5
10
15
0 5 10 15
North and South
0
5
10
15
0 50 100
Around 3
0
5
10
15
0 50 100
Around 4
0
5
10
15
0 50 100
Around 5
0
5
10
15
0 50 100
Around 7
0
5
10
15
0 50 100
Around 10
0
5
10
15
0 50 100
Around 11
0
5
10
15
0 50 100
Around 12
0
5
10
15
0 50 100
Around 15
0
5
10
15
20
25
0 50 100
West North
0
5
10
15
20
25
0 50 100
West South
0
5
10
15
20
25
0 50 100
East North
0
5
10
15
20
25
0 50 100
East South
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome W and NW
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome N and NE
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome S and SW
0
5
10
15
20
25
30
35
40
45
0 50 100
Main Dome E and SE
Hei
ght i
n m
Amplification Factor
2.0264Hz
After
NS
DW DN
DS
NW
SW SE
NE
1F
2F
3F
D
N
S
W E
100
15
15
100
100
100
100
-7.8%
Amplification Mode of 2nd Modal Frequency (NS comp.)
This figure shows the amplification mode of the 2nd modal frequency and the
characteristics do not differ from that of 1st modal frequency as a trend. The characteristic
point of 1st and 2nd mode is large amplification related to the SW main pier, and it is obvious
especially for the NS component. This problem on the SW main pier has been pointed by
Durukal et al. (2003) based on the analysis of the earthquake motion records, and is also
clearly appeared on the characteristics of microtremor.
NW corner NE corner NW
buttress pier
NE
buttress pier
SW corner SE corner SW
buttress pier SE
buttress pier
NW
2nd Pier
SW
2nd Pier
NE
2nd Pier
SE
2nd Pier
System and Data Research
dj: Displacement at jth Floor
dj = Ajag/wn2
= Ajag/(2pfn)2
gj: Drift Angle at jth Layer
gj = (Aj – Aj-1)/hj/(2pFn)2ag
= Kbjag
Kbj = (Aj – Aj-1)/hj/(2pFn)2
ag: PGAAj: Amplification Factor at jth FloorFn: Natural Frequency of the Buildinghj: Height of jth Layer
A
A
A1st Floor
nth Floor
jth Floor
Ground Floorg1
gj(j-1)th Floor hj
Seismic Acceleration ag
dj
Large K-value means that the portion is vulnerable.
On the Kb-value <a Destructive Index>
Please see the detail of Kb value on reference below as a name of KT. => Nakamura, Y. and et al.(2000):
Vulnerabiliy Investigation of Roman Collisseum using Microtremor, 12th WCEE, paper #2660.
This is
explanation of Kb-
value. It can be
used for
estimation of drift
angle for each
floor by Kb-value
times PGA, peak
ground
acceleration.
System and Data Research
Kb values at 1st Modal Frequency (EW component)
Although Kb value becomes small after the earthquake, the trend to be large at west or south side has
not changed. It is obvious that west or south part is weak point from the past earthquake damage or
other deformation situation, and it is possible to say that the microtremor reflects the structural
characteristics well. Points with large Kb value after the earthquake are at two sub piers and two main
piers of the west side and the dome cornice at west side. it is considerably to become larger at the
points on the western half dome related to the damage for the half dome of west side and west part of
the main dome caused by the earthquake in 10th century.
E
SE S
SW
W
NW N
NE
N
3F1 3F2
3F9
3F8
3F13 3F14
3F6
3F16
-50
-40
-30
-20
-10
0
10
20
30
40
-10 0 10 20 30 40 50 60 70 80
グラフタイトル
NW
2nd pier
SW
2nd pier
NE
2nd pier
SE
2nd pier
NW
main pier
NE
main pier
SW
main pier SE
main pier
NW
corner
SW
corner
NE
corner
SE
corner SW buttress pier SE buttress pier
NW buttress pier NE buttress pier
1.9043Hz Before
300 900 600
scale
E
SE S
SW
W
NW N
NE
N
3F1 3F2
3F9
3F8
3F13 3F14
3F6
3F16
-50
-40
-30
-20
-10
0
10
20
30
40
-10 0 10 20 30 40 50 60 70 80
グラフタイトル
1.7578Hz After
Dome-3F
3F-2F
2F-1F
100 300 200
scale
System and Data Research
E
SE S
SW
W
NW N
NE
N
3F1 3F2
3F9
3F8
3F13 3F14
3F6
3F16
-50
-40
-30
-20
-10
0
10
20
30
40
-10 0 10 20 30 40 50 60 70 80
グラフタイトル
E
SE S
SW
W
NW N
NE
N
3F1 3F2
3F9
3F8
3F13 3F14
3F6
3F16
-50
-40
-30
-20
-10
0
10
20
30
40
-10 0 10 20 30 40 50 60 70 80
グラフタイトル
NW
2nd pier
SW
2nd pier
NE
2nd pier
SE
2nd pier
NW
main pier
NE
main pier
SW
main pier SE
main pier
NW
corner
SW
corner
NE
corner
SE
corner SW buttress pier SE buttress pier
NW buttress pier NE buttress pier
2.1973Hz 2.0264Hz Kb value at 2nd Modal Frequency (NS component)
Kb value of 2nd modal frequency becomes large at south side, west side and the dome. It
suggests that there must be a weak point from the characteristics of NS component.
Especially the Kb value of the main pier at south-west part becomes larger after the
earthquake for both EW and NS component, and it indicates a possibility to be suffered
some damage. And Kb value becomes dominantly small after the earthquake for the NS
component at south-west and south side of the dome, and it is because the difference for
the response of the dome becomes small by enlarged response of the south-west main pier.
Before After
Dome-3F
3F-2F
2F-1F
100 300 200
100 300 200
scale scale
We had an opportunity to measure microtremor at Hagia Sophia museum before and after the
Kocaeli earthquake 16 years ago by chance. As a result of the comparison of the
characteristics of microtremor before and after this earthquake with a focus on the
microtremor characteristics after this earthquake, it was found as follows;
The vibration predominates toward to the east-west direction as the main axis of the building.
Although this building has almost symmetrical structure for north, south, east and west as a center
of the center dome, the vibration mode shows that it is easy to shake at the west and south sides.
Vulnerability index for structures Kb value suggests that the west and south parts may be a weak.
From the change before and after the earthquake, although the amplification factor decreased
remarkably for the EW components, the trend to shake easily around the west side of the dome
does not change.
The SW main pier has a possibility to be suffered some damage caused by the Kocaeli earthquake.
As a result of our microtremor measurement 2 months before and 3 weeks after the Kocaeli
earthquake, the predominant frequency decreased about 8% after this earthquake.
The result of the microtremor measurement suggests being high risk around the west half
dome and it agrees with the past researches. It is expected to expose the weakness of the
buildings by the characteristics of the microtremor.
System and Data Research
Concluding Remarks
System and Data Research
Acknowledgements
On the measurement of Hagia Sophia museum, I feel I owe
a great deal for Prof. Erdik of Bogazici University, director
of the museum and other concerned personnel.
I greatly appreciate their help.
Thank you for your attention!